Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C52 ⋊ #101 |
77 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^5,5^2|a^2=e,b^2=d,d^2=e,b^a=bc,d^a=de,f^a=f^4,g^a=fg,c^b=ce,f^b=f^2g^4,g^b=f^3g^3,f^c=f^4,g^c=g^441 conjugacy classes — view the full character table.
| maximal subgroup of | #13104165, #13104166, #13104167, … |
| maximal normal subgroup of | #13104165, #13104166, #13104167, … |
| maximal quotient of | #13099960, #13099968, #13099970, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 445);